Buscar

A diferença entre o pedreiro e o engenheiro

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Prévia do material em texto

Métodos Formais: A diferença entre o pedreiro e o engenheiro 
 
Paulo Borba 
Departamento de Informática 
Universidade Federal de Pernambuco 
 
�
� � � � �� � � ��	 �	 �
	 �� � �
 � � �� 
�� �
 	 �	 ��	 � � ��� �
 �� �� �� �� �� � � �� � � 	 ��	 �� � � � ��� � � � �� 	 �� � 	 �� 	 � 	 � �� � �
�	 � � � � �� � � �	 ��
� � 	 �
	 ��� � 
� �� � � ��� � ��� �� � � ��� �	 �
� � � ��� � 	 �
 	 ��� �� � � �� 
� �� � 	 � �� � � 
 � �	 � 
� � 	 
� �
� � � �	 �� 	 �� � � �� �� � � � � � � �� 
� � � �� � 	 � � � ��� � �
 � � � � � �
 �
� � �
 
� � �� 
� � ���
� � � � � 	 � �� �� � � � � �� � �
	 � �
� � 	 � � � �
 � ��� � �
 � � �� 
�� �
 	 �	 �
 �� �� �	 ��� �� � � � ��� 
��� � 	 �� 	 � 	 !��
�
" � � � �� � � �� � �	 �� 	 � 	 �� �
 	 �	 �� �� 	 � # � ��� �� 	 ��	 � ��
	 !!!�$ � �� � �� �� � ��% 	 �� �� �
 	 �	 �
� �� �� 	 �
� 	 ��	 �
 	 � 	 �
	 �
� 	 �� � � 
� 	 !�& � � � � � �� 	 � � � � � 	 � � � ��
 � � �� 
�� �� �
 �� ' �	 � 	 � � ��( � �
 # 
��� � � �� � !�) �� �� � � � � �� � � � �
�� � � �� � �
	 ��� � � �� � �
 � � � � �� � �� 
� 
 � � 
� � � �
 	 �	 �� � �	 ��	 � �� � � � ��� �� � � # � � 
� � � �� � �� * � 
� � � �� � �
 �� ' �	 � 	 � � � �
� 
 � �	 �
� 	 !�& � �� 	 �� � � �� ��� � � 
� � 	 !�+� � �� � 
� � �
 	 �	 �� 
� �� � 	 � �� 	 
� �� � � 
 �� , � � !�� �� �
�� � � ��	 � � �� �	 � � 
�* � � ���	 
 � � 	 ��� � �- � �� � � � � �� � ��
��
�	 � �� �� ���� � ��	 � �� !�� � �' � �	 ��� ��� �� �* � � �� � � �	 �� 	 � 	 �
� � �� 	 � # � ��� �� � � 	 � � ��� � � � � �� � � �� � 
�� ��� � ��� , �� �� ���������
 �� � 
�� �� � ��� � � � �� * ' 
� 	 ��
�� 
 � � �
� 	 � � � �� �� � � 	 
 	 �� � 	 � �� 	 ��� �	 �
 � �� � � � � �	 �' � � 	 � �
� �� �� 	 � . � � �� ��� � � � � � � �� � ��
�� 
� 
� 
	 �
� 	 � � � ��� � �� � � � ���
�
& � �� � �	 � �� ��� �� 	 ���� � � 
� � 	 � � � �� �� � �� � �� 
� �� � 	 �� �
� 	 � � 
�* � � �� � 	 � � � �� � �� � �� � ��� ' � �	 ��� � �
� � � � �
� � � �� � �� �� � �� 
� � � �� � � � � � 
	 
� �- �
 � 
 � �	 � � � !�� � ��� , � � 
 �� ��� � � ��� �� �� � �
 �� � � � � � �
� � � � ��
	 ��� �
� � ���* �� ' � �	 � �� � ��� � � ��	 
� ��� �� �/ � 
� 	 � �� �� � � �� 	 �� � ��� � � 
 � �	 � � �� � �� � �� � �� � �� � �� 	 �� �
�� � �� �	 � 
. � � ��� �
� 
� �� � 	 � �� 
' 
�	 
� �� � � 
� 	 � � � �0� � � � �� � � � �� � � ��� �	 �� ���� 
� �� � �	 �
� �� � � � �� �� ��/ � 
� 	 �� � � �� 	 ��� � 1��� � �
 � � ��� � � 
� � 	 ��� � �	 � � �� � �� � � �	 � �� � 	 � �� � 
 � � 
�
� 	 � . � � !�& � � �� � �� 	 � � � ��� ��� � � 	 � � � �	 ��	 �� �
�
� 	 � � � �� � �
2 � �� � � � �3 � �� 	 
� �� � �� � � � � � � �� 
� � � �� ��� � � � 	 
� �� � � �� 	 � � 	 � � � �� � �
 �
� � �
 
� � �� 
� � ���
� � � �� �
' 	 �	 � �� � �� �� � ��� �� ��� � � 
� � 	 � � � �� �� � � �� 
� �� � 	 � � 	 �� � � � 	 ��� �� 	 � � � �� � �� � ' � � # � 
�� �' 	 �	 � �� �
 � � �	 �� � 	 �� 	 � 	 �� � � �� � � 	 � 	 �* �� � � �	 �
 �
� � 
�	 �� # � � 	 �� � �� � �� � !��
�
2 � �� � � � ��� �� 	 
� ��	 � � � �� � � � � � �
 �� ' �	 � 	 � � �� � ���	 � 	 �# � � �� � � � �� � ' � � # � 
�� � �� �� � � �� � � � �
 � � �� 
�� � !�4 � � �� � ' � �	 � � 	 ��� �� � � �� � �	 ��	 � �� � � � !�2 	 � �� � � � �� 	 �	 � �� �
� 	 �� � �	 �� 
�� �� � � 	 � �� �
� � 
�� ��
� �� � � � � � � �� 
� � � �� ��� �� 	 ���� � � ��	 �� �
�
� 	 � � � �� � ��
� ' � 	 ' � � � �0� � �	 � * �
� � ��� � 
 � � 
�
� 	 � � � ��
 �� �� �� ��� �
� 
 �� � � � �	 � � � 1� � � ��� � # 	 � �� � 	 �� � � 5 � �
� 	 �� 	 �� � * �
� 	 �� � � �� � �
� 
� 	 ��� � � �� � 
, 	 � � � �� 6 � 
� 	 � �
 � 	 � �� �	 � �� 
' � 
�
� 	 � � �� �� � � 
 � ��	 � � � �� �� � �� 7 � 
' � �� � � �
�� !�) � � 
� �� �
 �� ' �	 � 	 � � ���� � �� � ' � �	 � � 	 �
� � � � � �� 	 � � �� , 	 �	 � � � �� �� � � � �� � �* �� � 
 � � 
�
� 	 � � � �� �
� 
 �� � � � �	 � � � !��
�
8 � ' � � � � ��� � �� � �� � � � ��� �� 	 
� �� �� �� � � � ��� � � �� � � �
 	 �	 �' 	 �	 � �
�� � � �� � �# � �	 � � � �� � �� 	 �� � � � �
� � � �
� � �� � �� 
� �� � 	 �
 �� � � �� 	 � �� �� � � 
 � ��	 � � � �� �� ��� � � 
� � 	 �
� 	 � � �� � �� � � � � !�� � ��	 � �� �� �
 �� ' �	 � 	 � � ��
� 
� 
 . � �� � �� � 	 ��� � �� �� � ' � �	 �
 	 �	 �' � 
	 ��� � � 	 � � 	 � �� 	 �� � ��� �� �	 �� 	 �� � 
 � � 
�
� 	 � � � ��� � ��� � �
�
� 	 ��	 �
��� � 	 �� � �� � 	 �
� 
 �� � � � �	 � � � �� � � � � �� �
� 
� � �� �
 � ��� � 	 �� 	 
� �� �
� 
� � �� ��� � �# � �	 � � � �	 � � 	 �
� 	 � � �� � �
� 
� �� � 	 �� ��� � � � �	 �� � ��� � 	 �� � � � � �� ��� � �� � � �� � � �
� ��� � � � 
� � � !�
�
) � � 
� �� � � � �# * �� 	 � �	 ' � � � �� � �� � � ��	 �	 ��� � �	 � � 
�� �� �� �� � �� � ' � � # � 
�� �
 	 �	 �
 �� �� �	 ��� � 	 �� 	 � 	 ��
� � ��	 � � � �� �# * �� 	 � �	 ' � � � �� � �� � 	 ��� � �� � � � ��� �� 	 
� !�� � ��� , � � 
 �� ��� � � 
� � �- �
 �� � 
� � � �� 	 � �
�
� ' � 	 ' � � � �� �
�
� 	 � 	 � ��	 � �� � 
 � � 
�
� 	 � . � � �� � � �� 
� �� � 	 � �� � � �� � � � 
� �� � �� � �� ��
� �� � �� � �	 � � 
' 9 
� 	 � � � ��
 � � � � � � �	 �� �� � �� 
��� � � � �� � � ��	 �� � 
 � ��� , � � 
 �� ���	 � �� �� � ��� �� �� �
� � �� �� �� ��� �� � � � � � ��� � �� � ��% 	 �� �
 � 	 � �� �� � ��� �� �	 � 	 �
� �	 �� �� �
 �� ' �	 � 	 � � �!�( � � � 	 ��� �� 	 �� 	 � 	 �� � � � �� �� � �� � 	 �� � 
 � �� � �
� � � � � � � �� 
� � � �� �� 	 � � �� , 	 �	 � � � �� �� � 	 � �� � �
' 	 � . � � �� �� � � � �
 � � � �� � 
 � �	 ��� � � �� � ��� � !�� � 
�	 :� � �
� � �� � ��	 �# 	 � �� 	 �� � � � � 
� 	 � � � �� � ��� �� � �� � � � �� � ��� � � � �� �� � 	 �� 	 � �
 �
� � 
 	 
� �� 	 � � 	 � �
 	 �	 �	 ��	 � � � �
� � �� � � � � � � �� 
� � � �� �� �	 � � � � �� �� � � �� � � �� � !��
�
� � ��� � ��� ��	 � � ��� � � 
� � �	 � �� � 
 � ��� �
 	 �	 �� � �# � �	 � � � �� �� 	 � �� � � � �
� . � � ��
 � � � :� � �' 	 �	 � �
�� � � �	 �
� 
 �� � � � �	 � � � ��
� 	 ��� � �� 
� �� � 	 �� � ��� � 
 � � � � �- �� � 	 �� � 
 � � 
�
� 	 � � � �
� 
� 
	 ���� � � � �� �� � � � � � 
	 ��
 	 �	 �
 � � �� �� 
� �� � 	 ��� � � 
� � � �� � � � ��� � 
� 
�	 � � �
 � �� �� �
� � �� �� � �� � � * �
� !�$ � �� � �	 ��
 � � � :� � �' 	 �	 � �
�� � � �� �
� 
� �� � 	 �� �� � ��� �� �� ��� � � � �� ���	 �� �� � � � � �� � � � � �� � ��� � � � �� 	 � � � �� � � � 	 � � � ��� � ��% 	 �� �� � �
 � 	 �
� 	 � � ��
 �
� � 
 	 �� � � �� �
 � ��� � �� � �� �	 �	 � � � �� �� 
� �� � 
� �� ��� �� � �� � �
� 
 	 � �� �� 
�� �� �� � �� � �
� 
	 � � �
� � � �� � � * �
� � !�� �� 	 �� ��� � � �	 �� � � �	 � � 	 �
� 	 � � �� � �� � ��% 	 �� ��� � �� � 	 �' �	 � � � ��� �� � 5 � � 
	 �� � � � / � 
� 	 �
� �� � � 
	 ���� � �� �� 
� 	 � � � �	 �� � � 
 � �
�
� 
� 	 � � ��	 � �� �� 	 � �� � 
 �� � 	 � � � � �
 �� � � � � � �� �� � ��% 	 �� � � 	 � �� �
� 	 � � � � �� � � � � � � � !��
�
2 	 � �� � �
 � � �� 
�� �� � � �	 �� � � � � �
 � �� �� � � ���	 � 	 �# � �� � � � � �� � �� � ' � � # � 
�� �� � �� � �	 � � 
�� �� !�" � � � � �
� 7 � �� 	 � � � � � �� � �� � �
� � � !�8 
� 
�	 �� � � �� ��	 �� �
�
� 	 � � � �� � �� � �� � � � ��� �� 	 
� ��� � ��� � � ��� � � �	 �� 	 
� �� � �
 � � �� �� � � �� � �� � �� � � � ���	 � 
� 
� � 	 
� �� � �� � � � � � � �� 
� � � �� !�� � ��� �� � ��	 � ��	 � . � � ��
� �� �� , 
 �
� 	 �
 � � � � �
� � �� � �� � � � ��� �� 	 
� �	 
� � 	 �� � � �� � � ��� � �� 
�� � � 
� � � �� 	 �
� � 6 � ��
	 !�) � � 
� �� � � � �� 	 �� � � � �# 	 �� � ��� �� �
 � � �� 
�� �� �� �� � ' � � # � 
�� ���� � � � � � � �	 � 	 �
� 	 ��� � � �� � 
� 	 � � �� � �	 �� � � � � � 
	 �� 	 �� �	 �
 � � 	 �	 ��� � ' � �
 �	 � � !�& � � �	 � 
	 � �	 �
 	 ' 	 ��� 	 �	 �� �� � �	 �� 	 � 	 �� � � 	 � 	 �� � ��	 �
 �
� � 
�	 �� # � � 	 !�$ �� � � � � � �� �
 � � � �� 	 
��
� 	 �� �� � � 	 
� ��8 � �* � � � �	 � �� � �
� 
� � � 
	 � �� � ��� � � 
� � 	 � � � �� �� � �� 
� �� � 	 �� � � ��� �� �* � � 
� �� ��� � �
�
� 	 � �	 �
� � � � � � 
	 � �8 � �� � �� �� � � ��� ��� �� 	 � � ��� �� � �# � ��� � � �� � � ��	 �	 ��� �
 � � �� 
�� !�( � ��	 �� ��� * �
	 � �� � 
 �� � 	 � �
� � � �� � � � � 
� 	 � ��� � �� � � � � � � �� 
� � �� 
� �� � 	 � �� ���
� � � �� �
�
� 	 � � � �� � �� � � � ��� �� 	 
� �� 	 �
 �* �
� 	 !�� �	 �� �
� � � � � �� � � � � � 
� 	 � � � ��; 	 � �	 �� �# 	 ��� �� 	 � � �� 	 �< 	 = �# � � � ��� � � � � � � �	 �� 	 ��
� 
�	 � � � �
 	 �	 �
� 
 �	 � �	 ��� �
� 
� �� � 	 �� � ��	 � 	 �� � �� 	 �) � 	 � / � 
	 �� � � �� � � � � ' � 
� �� � � � � � 
� 	 ��> ? �� 
�# . � � �� � �� 7 �	 �� � ��� � �� � �
 � ��� � � �� � �@ �	 � � � ��� � � 
� � �	 � �� � � �� � �� � �� � � � ��� �� 	 
� !�) � �� � �� � � �� � �� � � � ��� �� 	 
� ��A B C �� � �� � � �� �
� � �� � �� 
� �� � 	 �� 	 �< 	 = �# � � � �� � ��� � 
 � � � 
	 �	 � �� � �� �� � �� � � � � � * �
� �
 	 �	 �� � ��
' 
��� � �� ��� � �� � �� 
� �� � 	 !�
D � �� �� � �� �
 � �� � � �� 	 ��� � � � � ��	 :� � �	 � 	 
, � �� � �> B C !�� � �
� ��� � � ��	 �	 ��� � �� � ' � � # � 
�� �
 � � � �� � ��� � �
� � � �� � ' 7 � 
� ��

Outros materiais